HD800 is my favourite... Even K701 fails to compare. But K701 over HD650 any day...
What I use to judge whether something sounds "natural"... After I heard the HD800 it has become my benchmark of some sort. Go listen to "Somewhere Over The Rainbow" by Jane Monheit on the Best Audiophile Voices album... The piano is distinctly out of tune on the HD800, only a bit obvious on the K701 and virtually undetectable on anything else.
That's what I really like about them. Especially since I play jazz and classical a lot, I know the sounds of the acoustic instruments, and even plugged in instruments, very well. If you want to talk about accurate reproduction of "plugged in" music. Best is to listen to the artist live and see if that tone is the tone that you get from your headphones, because that's what he likes and wants you to hear. =) So even with electric instruments it's highly possible to do so.
I think that the most important thing to "natural sound" would be what is "natural" to you. I really wonder how many people who comment and use hifi equipment actually play/listen to live music. I think these are critical factors.